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Novel Finite Element Technologies for Solids and Structures [electronic resource] / edited by Jörg Schröder, Paulo de Mattos Pimenta.

Contributor(s): Schröder, Jörg [editor.] | de Mattos Pimenta, Paulo [editor.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: CISM International Centre for Mechanical Sciences, Courses and Lectures: 597Publisher: Cham : Springer International Publishing : Imprint: Springer, 2020Edition: 1st ed. 2020.Description: VII, 197 p. 133 illus., 85 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783030335205.Subject(s): Mathematics—Data processing | Engineering mathematics | Engineering—Data processing | Mechanics, Applied | Computational Mathematics and Numerical Analysis | Mathematical and Computational Engineering Applications | Engineering MechanicsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 518 Online resources: Click here to access online
Contents:
Notes on Basic Concepts of the Finite Element Method for Elliptic Problems -- Sensitivity Analysis Based Automation of Computational Problems -- Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity -- A Concept for the Extension of the Assumed Stress Finite Element Method to Hyperelasticity -- Simple Equilibrium Finite Elements for Geometrically Exact Bernoulli-Euler Beams and Kirchhoff-Love Shells -- Isogeometric Analysis of Solids in Boundary Representation.
In: Springer Nature eBookSummary: This book presents new ideas in the framework of novel, finite element discretization schemes for solids and structure, focusing on the mechanical as well as the mathematical background. It also explores the implementation and automation aspects of these technologies. Furthermore, the authors highlight recent developments in mixed finite element formulations in solid mechanics as well as novel techniques for flexible structures at finite deformations. The book also describes automation processes and the application of automatic differentiation technique, including characteristic problems, automatic code generation and code optimization. The combination of these approaches leads to highly efficient numerical codes, which are fundamental for reliable simulations of complicated engineering problems. These techniques are used in a wide range of applications from elasticity, viscoelasticity, plasticity, and viscoplasticity in classical engineering disciplines, such as civil and mechanical engineering, as well as in modern branches like biomechanics and multiphysics.
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Notes on Basic Concepts of the Finite Element Method for Elliptic Problems -- Sensitivity Analysis Based Automation of Computational Problems -- Equilibrated Stress Reconstruction and a Posteriori Error Estimation for Linear Elasticity -- A Concept for the Extension of the Assumed Stress Finite Element Method to Hyperelasticity -- Simple Equilibrium Finite Elements for Geometrically Exact Bernoulli-Euler Beams and Kirchhoff-Love Shells -- Isogeometric Analysis of Solids in Boundary Representation.

This book presents new ideas in the framework of novel, finite element discretization schemes for solids and structure, focusing on the mechanical as well as the mathematical background. It also explores the implementation and automation aspects of these technologies. Furthermore, the authors highlight recent developments in mixed finite element formulations in solid mechanics as well as novel techniques for flexible structures at finite deformations. The book also describes automation processes and the application of automatic differentiation technique, including characteristic problems, automatic code generation and code optimization. The combination of these approaches leads to highly efficient numerical codes, which are fundamental for reliable simulations of complicated engineering problems. These techniques are used in a wide range of applications from elasticity, viscoelasticity, plasticity, and viscoplasticity in classical engineering disciplines, such as civil and mechanical engineering, as well as in modern branches like biomechanics and multiphysics.

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